1. Rising Fuel Prices and the Potential of Input Substitution in US Corn Production Henry Thompson, 1 Osei-Agyeman Yeboah, 2 & Victor Ofori-Boadu. 2 1 Auburn University 2 North Carolina A&T State University

2. Motivation Energy prices are projected to continue a slow increase over the coming decades as reserves of oil are depleted There is no doubt that rising diesel prices will play a role in agricultural production decisions over the coming years Outcomes of energy policies often hinge on energy substitution but there is little consensus on energy substitute Berndt and Wood (1975) find energy a substitute for labor but complement with capital while Griffin and Gregory (1976) find energy a substitute for both labor and capital

3. Background This study estimates energy substitution in US corn production from 1975 to 2004 in a translog cost function Cross price elasticities describe the adjustment in capital, labor, energy and fertilizer inputs to the price of energy as well as the adjustment in energy input to the other factor prices The findings of this study is to give some idea of the potential to substitute other inputs for energy as energy prices rise over the coming decades

4. Input substitution in agricultural production There are numerous input-output relationships in Agriculture since the rates at which inputs are transformed into output vary among soil types, animals, technologies, rain fall amounts etc. The Leontief production function for example, has the property that, a decrease in the utilization of any input implies that output will fall, no matter what happens to the utilization of other inputs. However, it has been long observed that decreased utilization of one input may be compensated for increase utilization of another input.

5. The ability of one input to compensate for another has been found to be significant in most farming operations. It is therefore possible to produce a constant output level with variety of input combinations The importance of input substitutability has led to the definition of various elasticities of substitution providing unit-free measures of the substitutability between inputs Input substitution in agricultural production

6. The theory of energy substitution Energy input involves work that transforms matter and includes fuels based on natural resources Energy substitution starts with the production function x = x (K, L, F, E) The firm or industry is assumed to produce the profit maximizing output x* hiring the optimal inputs of capital K, labor L, fertilizer F, and energy E that minimize cost of production

7. The theory of energy substitution The model assumes competitive price taking in the input and output markets and comparative static substitution between energy and the other inputs given cost minimization Shephard’s lemma states that input levels are derivatives of the cost function c(r, w, e; x) with respect to input prices. Thus E* = δc/δe

8. The theory of energy substitution Estimation of cross price elasticities can begin with the translog cost function (TCF) Fuss and McFadden (1978) and Saicheua (1987) where w i is the price of input i, r is the price of capital, w the wage, f the price of fertilizer, e the price of energy, and t represents technology

9. The theory of energy substitution The elasticity of cost with respect to the price of energy is the partial derivative of the TCF with respect to the price of energy δlnc/δlne = c E + c KE lnr+ c LE lnw + c EE lne + a E t (2) By Shephard’s lemma, E = δc/δe and δlnc/δlne = (δc/δe) (e/c) = E (e/c) = eE/c For a competitive firm, cost c equals revenue c = px = x. It follows that δlnc/δlne = eE/x = θE, making (2) the energy factor share equation

10. The theory of energy substitution Factor share equations for the other inputs are similar, leading to the cost share system (See equations below) (3) Estimates from the above equations provide the coefficients to derive substitution and cross price elasticities

11. The theory of energy substitution The second cross partial derivative of the TCF for energy price e and labor prices w is used to solve for their cross price elasticities ε EL = (c EL + θ E θ L )/θ E (4) Own price elasticities are derived as: ε ii = (c ii – θ i + θ i 2 )/θ i (5)

12. Data Historical data from 1975 to 2004 on per unit price, quantity of corn produced, labor, fertilizer, and energy used in corn production were obtained from USDA/ Economic Research Service online database. The shares of the four inputs are plotted in Figure 1. Capital share is declining as the others increase. Especially energy and fertilizer shares increase during the period. Fertilizer is an energy-intensive product and its price and factor share may move along with those of energy. Figure 2 shows the history of factor prices. Fertilizer prices have indeed risen during the period, while energy prices have been stationary or slightly declining

13. Figure 1. Factor Shares

14. Figure 2. Factor Prices

15. Results Below are the estimated factor share equations:

16. Results The null hypothesis of continuously improving technology cannot be rejected in any of the factor share estimates The overall explanatory power of the factor share regressions is fairly high and autocorrelation of the residuals is not a problem Only 2 of the 16 factor price coefficients in (6) are significant but the present goal is estimation of substitution elasticities and the coefficients are used in the calculations

17. Results Constant returns CRS implies the sum of the constant terms is one and but the sum of the estimated coefficients is 0.96 CRS also implies the sums of the factor price coefficients in the four factor share equations should equal one but these sums are  K =.412,  L = -.195,  F = -.292, and  E =.072 This suggest a decrease return to scale in corn production. Corn farmers could lower all inputs and total cost would fall by a lower percentage than output

18. Results The derived matrix of substitution elasticities following (4) and (5) is  KK  KL  KF  KE-0.33 0.36 0.51 0.04  LK  LL  LF  LE = 0.90 -3.38 -2.06 0.21  FK  FL  FF  FE 0.81 1.03 -1.44.002  EK  EL  EF  EE 0.92 1.32 -0.18 -0.75 There is limited substitution potential when energy prices rise in fuel production The own energy substitution elasticity of -0.75 implies that a 10% increase in the price of diesel will reduce diesel input only 7.5% and expenditure will rise 2.5%

19. Results The results show a weak substitution toward labor input with labor input rising 2.1% There is virtually no substitution of capital or fertilizer for energy Corn producers respond more to rising wages. If slower labor immigration raises wages on the farm by 10% there would be a 33.8% reduction in labor input and a 23.8% reduction in the labor bill There would be strong substitution toward energy input with a 13.2% increase. Corn farmers can substitute energy for labor to a high degree Fertilizer substitution has near unit value and fertilizer input would match the wage increase in percentage terms

20. Results There is much less substitution of capital for labor Combining a 10% increase in the wage due to tougher immigration policy with a 10% increase in the price of energy, labor input falls 31.7% and energy input rises 4.7%. The labor bill would fall 21.7% but the energy bill would rise 14.7% Higher fertilizer prices have an elastic own effect with enough substitution that fertilizer spending falls with a higher price. Labor and energy inputs also falls with higher fertilizer prices Energy input substitutes for capital and labor but is a complement with fertilizer

21. Conclusion The present estimates predict corn producers will spend more on energy as energy prices rise An increasing price of diesel only inelastically lowers diesel input while raising labor input Corn farmers are sensitive to wages, however, they will substitute energy for labor as wages rise The combination of tougher immigration laws with rising diesel prices leaves little room for substitution The estimated decreasing returns to scale suggests overproduction of corn If subsidies are cut as fuel prices rise over the coming decades, the present model of substitution predicts a substantial decrease in US corn production